47
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Spectral stability of periodic traveling wave solutions for a double dispersion equation

&
Received 10 Jul 2023, Accepted 10 Apr 2024, Published online: 27 Apr 2024

References

  • Bronski J, Johnson M, Kapitula T. An instability index theory for quadratic pencils and applications. Comm Math Phys. 2014;327:521–550. doi: 10.1007/s00220-014-1949-5
  • Deconinck B, Kapitula T. On the spectral and orbital stability of spatially periodic stationary solutions of generalized Korteweg–de Vries equations. In: Guyenne P, Nicholls D, Sulem C, editors. Hamiltonian partial differential equations and applications. Vol. 75, New York: Fields Inst. Commun.; 2015. p. 285–322.
  • Grillakis M, Shatah J, Strauss W. Stability theory of solitary waves in the presence of symmetry I. J Funct Anal. 1987;74:160–197. doi: 10.1016/0022-1236(87)90044-9
  • Grillakis M, Shatah J, Strauss W. Stability theory of solitary waves in the presence of symmetry II. J Funct Anal. 1990;94:308–348. doi: 10.1016/0022-1236(90)90016-E
  • Hakkaev S, Stanislavova M, Stefanov A. Linear stability analysis for periodic traveling waves of the Boussinesq equation and the Klein-Gordon-Zakharov system. Proc R Soc Edinburgh A. 2014;144:455–489. doi: 10.1017/S0308210512000741
  • Kapitula T, Promislow K. Spectral and dynamical stability of nonlinear waves. New York: Springer; 2013. (Applied Mathematical Sciences; 185).
  • Stanislavova M, Stefanov A. Stability analysis for traveling waves of second order in time PDE's. Nonlinearity. 2012;25:2625–2654. doi: 10.1088/0951-7715/25/9/2625
  • Kolkovska N, Dimova M, Kutev N. Orbital stability of solitaryWaves to double dispersion equations with combined power-Type nonlinearity. Mathematics. 2021;9:1398. doi: 10.3390/math9121398
  • Iorio R, Iorio V. Fourier analysis and partial differential equations. Cambridge: Cambridge University Press; 2001. (Cambridge Studies in Advanced Mathematics; 70).
  • Byrd PF, Friedman MD. Handbook of elliptic integrals for engineers and scientists. 2nd ed., NY: Springer; 1971.
  • Eastham MSP. The spectral theory of periodic differential equations. Edinburgh: Scottish Academic Press; 1973.
  • Magnus W, Winkler S. Hill's equation. New York: Wiley; 1966.
  • Natali F, Neves A. Orbital stability of solitary waves. IMA J Appl Math. 2014;79:1161–1179. doi: 10.1093/imamat/hxt018
  • Neves A. Floquet's theorem and stability of periodic solitary waves. J Dyn Differ Equ. 2009;21:555–565. doi: 10.1007/s10884-009-9143-8
  • Wang Y, Mu C, Deng J. Strong instability of solitary-wave solutions for a nonlinear Boussinesq equation. Nonl Anal. 2008;69:1599–1614. doi: 10.1016/j.na.2007.07.006

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.